Bridging scales with thermodynamics: from nano to macro

We have recently developed a method to calculate thermodynamic properties of macroscopic systems by extrapolating properties of systems of molecular dimensions. Appropriate scaling laws for small systems were derived using the method for small systems thermodynamics of Hill, considering surface and nook energies in small systems of varying sizes. Given certain conditions, Hill's method provides the same systematic basis for small systems as conventional thermodynamics does for large systems. We show how the method can be used to compute thermodynamic data for the macroscopic limit from knowledge of fluctuations in the small system. The rapid and precise method offers an alternative to current more difficult computations of thermodynamic factors from Kirkwood-Buff integrals. When multiplied with computed Maxwell-Stefan diffusivities, agreement is found between computed predictions and experiments of the Fick diffusion coefficients for several binary systems. Diffusion coefficients were obtained by linking the Green-Kubo formulae to the Onsager coefficients. The formulae were used to improve/disprove empirical formulae for diffusion coefficients.